Concept:
The weapon of an ancient vampire lord, the blade of the thirst is imbued with the vampire's lust for blood.

Description:
A black longsword with a guard made up of 3 carved black roses; the guard is gripped thorned vines that extend from the roses and bind to the wielder's wrist.

Features:
Blade of the thirst confers proficiency for itself onto the wielder.
At the start of the wielder's turn the blade of thirst drains blood from its wielder, causing 1/2/3 damage to the wielder (player's choice); the sword counts as a +x weapon until the end of the turn, where x is the damage caused to the wielder.

4 Answers
4

There is precedent for a longsword-type weapon having both the Finesse and Versatile properties (Sun Blade). Beyond that, this is a +X Weapon that hurts you in order to use its properties, making it inferior in that regard to a normal +X weapon.

As a character levels up, taking 1-3 damage becomes an increasingly non-issue. One minor exploit is that if you attain Resistance to whatever damage type the sword does to its wielder (I'd go for Necrotic, since it is drinking blood), then you could use the sword in +1 mode at all times with no drawback. But the fact that it hurts you at all already makes it inferior to a basic +X Weapon.

If you want to shut down the 'Resistance' case, then make sure the damage dealt by the weapon is explicitly stated to be irresistible.

I would not suggest making it state that actual the damage taken by the wielder translates to the +X applied. While this would prevent resistance abuse, it would open the weapon up to Vulnerability abuse. If a character was made vulnerable to Necrotic damage and it followed that rule, they could boost the weapon to a +6.

This weapon would be fairly hard to abuse, because you must be attuned to a magic item to use its properties, so the blood drinking property could not be used on enemies. As mentioned above, it's basically inferior to a normal +X sword...though the Finesse on a Longsword does give Dex-based classes a viable two-hander option.

A few things other I will note in your description, however.

You do not specify the damage type dealt to the player. All damage in 5E is typed in some way...I recommend Necrotic to represent it drinking your blood

The description stating that it 'bind[s] to the wielder's wrist.' A player will possibly try to make the argument that a sword bound to their wrist makes it immune to disarming. This isn't a huge deal...but your description leaves that open to argument.

I will note that some degree of care should be taken if you hand this sword out at low level. I would rank it as at least 'Rare' and treat it accordingly (inferior to a +3 Weapon, which is Very Rare). At low level, the ability to spike your chance to hit by 15% for only 3 damage is well worth it for some classes--particularly bursty ones like Paladins who, at level five (with a single round to prepare) can drop 2 Attacks, 2 Spell Smites, and 2 Divine Smites in a single round...bumping their chance to hit by 15% would be a significant boon to such a character attempting to Overnuke a target like this. I am not saying this to note that it is unbalanced...simply that, like most high +X weapons, passing it out at low level can have a significant impact.

Note

It has been brought up that using a Versatile/Finesse Weapon may allow some cheese with a Rogue's Sneak Attack by taking a 1 level dip into Fighter for Great Weapon Fighting. This is a non-issue because GWF only applies to the actual, raw weapon damage...not to bonus sources like Sneak Attack, Smite, etc. See the Question here as well as the following Sage Advice quote:

Q: Great Weapon Fighting and Battlemaster' Sweeping Attack: may I reroll the 1 and 2 of the superiority die?
A: Great Weapon Fighting works only with the damage dice of the qualifying weapon.

Wouldn't having resistance to the damage cause it to still round up to 1? Take 1 damage, halved would be .5, rounded up to 1. If that's true, you could use it at +2 and take only 1 damage while get a better bonus for the same damage.
– bubbajake00Dec 6 at 17:38

2

@bubbajake00 D&D 5e rounds down on everything. That's a change from previous editions, which had some ups and some downs. 5e is consistently down.
– Michael W.Dec 6 at 18:22

2

@MichaelW. ah ok, I had just been reading the Wizard Arcane Recovery feature and it said to round up. From what I can tell after researching now, there are only 1-3 specific times you round up.
– bubbajake00Dec 6 at 19:00

8

You could also include "this damage can't be resisted" or "the bonus is equal to the damage taken" (so if you resist half of 2, you get a +1 sword).
– Draco18sDec 6 at 20:50

4

If resistances work, then vulnerabilities work too. So, get vulnerable to the damage type, take 3x2 damage, get +6 weapon
– MisamotoDec 7 at 8:51

Yes. There are ways to abuse this.

tl;dr The major abuse is Great Weapon Fighting + Sneak Attack

Figher-Rogue Abuse: Great Weapon Fighting + Sneak Attack

A finesse weapons is valid for sneak attacks. This would incentivize multiclassing fighter-rogue for a substantial damage bonus. The great weapon fighting style, greatly increases the damage output of a sneak attack as all 1's and 2's get a re-roll. This is only possible because of the combination of versatile + finesse that is not otherwise available.

Barbarian Abuse

Unless the damage is psychic, a barbarian taking the bear totem would be able to get a +3 weapon for 1 dmg/round. This damage would also automatically allow the barbarian to maintain rage.

Balanced?

Generally, no. This confers a martial weapons proficiency which steps on the toes of the martial weapons classes and the pact of the blade class feature. It breaks the attributes of a weapon type (long sword) which allows other class abilities to leverage it in a way other long swords cannot be used.

The avenue of Fighter-Rogue Abuse is contentious, as per the chat discussion. It has also be noted that the Sun Blade has the same Finesse + Versatility properties, and would also be susceptible to this particular abuse.
– Matthieu M.Dec 7 at 9:05

This weapon will kill its wielder

At the start of the player's turn the blade of thirst drains blood
from its wielder causing 1/2/3 damage (players choice); the sword
counts as a +x weapon until the end of turn where x is the damage
caused to the player.

If they get knocked unconscious in battle, this thing will, the way you've written it, keep draining the wielder of at least 1 HP per turn. Each time it does so, it counts as a failure on the Death Saving Throw, (See PHB ch 9, Damage and Healing) but does not obviate that turn's saving throw. They will take a minimum of 1 failure per turn, and failing the first Death Saving Throw will mean they will die. Best case, you allow them to do their natural saving throw roll prior to taking the auto-fail from damage, but even then, you are costing them one of their Death saving throw rolls.

PHB Ch 9: Damage with 0 Hit Points. If you take any damage while you have 0 hit points, you suffer a death saving throw failure

Your player takes at minimum one point of damage per turn with this weapon in hand.

I didn't cite a page number because I only have access to DND Beyond right now.
– MarkTODec 7 at 15:34

1

+1 for finding this issue, though resistance could eliminate the risk as discussed above
– PunintendedDec 7 at 17:18

This doesn't seem like a way to abuse the attributes of the weapon. This seems like a significant drawback from the curse or negative aspect of it.
– GrosscolDec 7 at 18:52

It could be considered the GM abusing it, in a way. Plus, it's a significant feature of the weapon itself, which is not as written considered 'cursed' If I asked a question and had an issue like this that was not strictly speaking part of the question, I'd still want it pointed out regardless. It's never fun to ask about something, get info that leaves out a very important, but not specifically asked-for information, and when it comes up and bites me in the butt, be told 'well you didn't ask that' afterward, if the person knew of the problem and kept silent.
– MarkTODec 7 at 20:35

At the start of the player's turn the blade of thirst drains blood from its wielder causing 1/2/3 damage(players choice); the sword counts as a +x weapon until the end of turn where x is the damage caused to the player.

You should take more care to specify that the damage caused to the wielder is the plus of the weapon. So "barbarian taking the bear totem" would take only one, but get only a +1 bonus.

I'm saying this because it seems to be what you intended (you're looking to close loopholes in your question). If you are okay with 1 dmg giving a +3 in some situations that's fine... it is still mostly less powerful than a straight +3 weapon.
(Mostly = except for "granting proficiency to the wielder." Maybe not relevant to your campaign.)

Cool concept - while I'm here I have a suggestion that you expand the backstory/description out so it won't work for Paladins or maybe even certain alignments due to its vampire lord association/origins.